This is the 2636th most frequent Russian word.
успели
"Успели" means "managed" or "succeeded in time."
Here 'успели' implies succeeding in being timely for the train departure.
Мы успели на поезд.
We made it to the train.
In this context, 'успели' denotes accomplishment within a time limit.
Они успели выполнить задачу до дедлайна.
They managed to complete the task before the deadline.
This usage of 'успели' reflects completing multiple activities within a period.